Annulus Area
A = π·(R²-r²)P = 2·π·(R+r)It is the region between two concentric circles — the shape of a washer, a ring, or a pipe cross-section.
The area is π multiplied by the difference between the outer radius squared and the inner radius squared. In plain terms: the outer circle’s area minus the inner one’s.
The perimeter adds both circumferences, because the figure has two outlines: the outside and the hole.
This is the frequent mistake. The area is not π times the squared difference of the radii — it is π times the difference of the squares.
An example shows the scale of the error: with an outer radius of 10 and inner of 8, the correct calculation gives π times 36. The wrong one gives π times 4, nine times smaller.
The intuition: an annulus is the subtraction of two areas, and area depends on the square of the radius. Subtracting radii before squaring reverses the order of operations.
- Pipe cross-sections, to compute the wall material area — used in strength and weight calculations.
- Washers, sealing rings and mechanical bushings.
- A circular track or bed around a central element.
- Floor area between a round column and a circular boundary.
Frequently asked questions
No. The correct order is to square each radius and then subtract. Reversing it produces a result far smaller than the real one.
Radii. If you have diameters, divide each by two before entering them.
Yes, that is the most common use. The outer radius is the pipe’s and the inner is the bore; the resulting area is the wall’s material cross-section.
Then it is not an annulus, and this formula does not apply. The resulting figure needs a different calculation.